MATTHIESSEN ON THE EXPANSION OF WATER. V.-On the Expansion of Water. [Abstract from a paper read before the Royal Society December 21,1865.1 ON re-determining the co-efficient9 of expansion of water they were found not to agree with Kopp’s and as his are results gene- rally used by chemists it may not be here out of place to give the new values. MATTHIESSEN ON TEE EXPANSION OF WATER. It was found that the expansion of water betweeu 4' and 100" the formula by32Oand 4'may conveniently be expressed between Vt = 1 -0'0000025300 (t -4) + 0*0000083890 (t -4)2 -0~000000011~3 (t -4)'s and between 32O and 100' by Vt = 0'999695 + 0.00000547248 -0~000000011260~~ The values calculated from these formulae for the volume OCCU-pied by water at different temperatures are given in Table I.from degree to degree together with the differences for each degree. TABLEI. -~~ ~ Volume Differ-To Volume Differ-Volume Differ-of water me per To. of water :nee per ,-,.' of waterTO. at To. 1". 13 me per 1". C. C. at To. at 'La. I-1.000355 69 1*022050 4 1~000000 -000006 37 1*006616 363 70 1-022648 -000598 5 1-000006 6 1~000028 22 38 1.006979 372 71 1.023252 604 7 1-000066 38 39 1*007351 379 72 1.023861 609 531 40 1*007730 388 73 1-024477 616 8 1'000119 9 1.000188 69' 41 1 008118 396 74 1*025099 622 10 1'000271 83 42 1*008514 404 75 1,025727 628 634 43 1*008918 413 76 1-026361 11 I -000369 110' 44 1,009331 420' 77 1*027000 639 12 1.000479 13 1-000604 12.5 45 1-009751 428 78 1*027646 646 14 1.000742 138 46 1.010179 1351 79 1-028296 650 657 15 1*000892 1501 47 1.010614 445 ao 1-028953 662 16 1.001054 1621 48 1:011{*59 4511 81 1*029615 668 17 1.001227 1731 49 1 *011510 459 a2 1.030283 673 18 1*001412 1858 50 1.011969 466 83 1.030956 19 1'001608 1961 51 1-012435 474 84 1,031634 6 78 20 1.001814 206 52 1.012909 482 85 1-032318 684 689 21 1*002029 215 53 1-013391 488 86 1*033007 694 22 1 002254 225 54 1-013879 4971 87 1-033701 699 23 1*002488 234 55 1*014376 503' a8 1*034400 704 24 1-002731 2431 56 1*014879 5111 89 1-035104 709 25 1.002982 2511 57 1-015390 5171 90 1.035813 714 26 1-003241 259 53 1-015907 525 91 1.036527 718 27 1-003507 2661 59 1 -016432 532' 92 1.037245 724 28 1.003780 273 60 1-016964 538 93 1 037969 728 29 1,004059 279' 61 1*017502 516 94 1.0386C7 30 1 -004345 286 62 1 -018047 552 95 1-039429 732 737 31 1-004635 290 63 1*018599 559 96 1.040166 32 1 004931 296 64 1.019158 566 97 1-040907 741 746 33 1-005249 318 65 1.019724 572 98 1-041653 34 1-0055'78 329 66 1.020296 578 99 1*042404 751 35 1.0059 I6 338 67 1-020874 585 100 1*043159 756 36 1-006261 345 68 1-021459 591 MATTHIESBEN ON THE EXPANSION OF WATER.The values obtained by different observers for the volumeR occupied by water at different temperatures the volume at 4O being taken equal to 1 are given in Table 11. TABLE11. Hagen.$ Matthiessen. T. Kopp.* Despretz.1. Pierre.$ --8 1 ~000000 1 ~000000 1 *oooooo 1 ~000000 1~000000 10 1 *000247 1.000268 1-000271 1 -000269 1-000271 15 20 30 1 -000818 1.001690 1 -004187 1 *000875 1.001790 1 *004330 1.000850 1 *001717 1.004195 1 *000849 1.001721 1 -004250 1 000892 1-001814 1:004345 40 50 60 1.007654 1.011890 1.016715 1,007730 1.012050 1 *016980 1 *007636 1.011939 1 *017243 1 *00’77ll 1 -011994 I*017001 1 ‘007730 1 *011969 1 -016964 70 1-022371 1 -022550 1 -023064 1 -022675 1-022648 80 90 100 1.028707 1,035524 1.043114 1 -028850 1 -035660 1.043150 1 029486 1.036121 1.043777 1.028932 1 *035715 1*042969 1 -028953 1*035813 1 -043169 It wilI be seen from the foregoing table that Kopp’s values are lower than the others; and bearing in mind that the co-efficient of expansion of mercury namely 0.000178,when deduced by means of these falls below that obtained by Regnault namely 0*0001815,but when deduced from my own namely 0*0001812 agrees closely with Regnault’s we are led toconclude that Kopp’s values must be somewhat incorrect.* Pogg. Ann. xcii. 42. .t. Ann. Ch. Phys. lxx 1. $ Ann. Ch. Phye. [3] xiii 325. Calculated by Frankenhoim Pogg. Ann. xcvi. 461. 0 Abhandlungen d. k. Acad. der Wissensch. zu Berlin 1866.